In the figure, not drawn to scale. UVWX is a square. WXY is an equilateral triangle and UW is a straight line. Find
- Four-fifths of ∠UZY
- Six times of ∠YWZ
(a)
∠XUW = 45° (Right angle)
∠ZXW = 60° (Equilateral triangle)
∠UXZ
= 90° - ∠ZXW
= 90° - 60°
= 30°
∠UZY
= 30° + 45° (Exterior angle of a triangle)
= 75°
Four-fifths of ∠UZY
=
45 x 75°
= 60°
(b)
∠YZW
= 180° - ∠UZY
= 180° - 75°
= 105° (Angles on a straight line)
∠YWZ
= 180° - 60° - 105°
= 15° (Angles sum of triangle)
Six times of ∠YWZ
= 6 x 15°
= 90°
Answer(s): (a) 60°; (b) 90°
